A particle of mass m is attached to an end of a light rigid rod of length a. The other end of the rod is fixed, so that the rod can rotate freely in vertical plane about its fixed end. The mass m is given a horizontal velocity u at the lowest point.(a) Prove that when the radius to the mass makes an angle theta with the upward vertical the horizontal component of the acceleration of the mass (measured in direction of u) is [g(2+3 cos theta)-u^(2)//a] sin theta (b) If 4ag ltu^(2) lt5ag, show that there are four points at which horizontal component of acceleration is zero. locate the points.

A particle of mass m is attached to an end of a light rigid rod of len

1.	A particle of mass m is attached to an end of a light rigid rod of length a. The other end of the rod is fixed, so that the rod can rotate freely in vertical plane about its fixed end. The mass m is given a horizontal velocity u at the lowest point.(a) Prove that when the radius to the mass makes an angle theta with the upward vertical the horizontal component of the acceleration of the mass (measured in direction of u) is [g(2+3 cos theta)-u^(2)//a] sin theta (b) If 4ag ltu^(2) lt5ag, show that there are four points at which horizontal component of acceleration is zero. locate the points.
Answer» ANSWER :The FOUR POINTS are represented by `theta=-0, pi cos^(-1)((u^(2)-2ag)/(3ag))` and `[2pi-cos^(-1)((u^(2)-2ag)/(3ag))]`